On Lp-strong convergence of an averaging principle for non-Lipschitz slow-fast systems with Lévy noise

We study L^p-strong convergence for coupled stochastic differential equations (SDEs) driven by Lévy noise with non-Lipschitz coefficients. Utilizing Khasminkii’s time discretization technique, the Kunita’s first inequality and Bihari’s inequality, we show that the slow solution processes converge strongly in L^p to the solution of the corresponding averaged equation